Digital Adsorption: 3D Imaging of Gas Adsorption Isotherms ......gas separation processes, such as...
Transcript of Digital Adsorption: 3D Imaging of Gas Adsorption Isotherms ......gas separation processes, such as...
Digital Adsorption: 3D Imaging of Gas
Adsorption Isotherms by X-ray Computed
Tomography
Lisa Joss∗ and Ronny Pini
Qatar Carbonates and Carbon Storage Research Centre, Department of Chemical
Engineering, Imperial College London, London, UK
E-mail: [email protected]
Phone: +44 20 7594 7518
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Abstract
We report on a novel approach for the measurement of gas adsorption in microp-
orous solids using X-ray computed tomography (CT) that we refer to as digital adsorp-
tion. Similar to conventional macroscopic methods, the proposed protocol combines
observations with an inert and an adsorbing gas to produce equilibrium isotherms in
terms of the truly measurable quantity in an adsorption experiment, namely the surface
excess. Most significantly, X-ray CT allows probing the adsorption process in three
dimensions, so as to build spatially-resolved adsorption isotherms with a resolution of
approximately 10mm3 within a fixed-bed column. Experiments have been carried out
at 25 ◦C and in the pressure range 1–30 bar using CO2 on activated carbon, zeolite
13X and glass beads (as control material), and results are validated against literature
data. A scaling approach was applied to analyze the whole population of measured
adsorption isotherms (∼ 7600), leading to single universal adsorption isotherm curves
that are descriptive of all voxels for a given adsorbate-adsorbent system. By analyz-
ing the adsorption heterogeneity at multiple length scales (1mm3 to 1 cm3), packing
heterogeneity was identified as the main contributor for the larger spatial variability
in the adsorbed amount observed for the activated carbon rods as compared to zeolite
pellets. We also show that this technique is readily applicable to a large spectrum
of commercial porous solids, and that it can be further extended to weakly adsorbing
materials with appropriate protocols that reduce measurement uncertainties. As such,
the obtained results prove the feasibility of digital adsorption and highlight substan-
tial opportunities for its wider use in the field of adsorptive characterization of porous
solids.
1 Introduction
Gas adsorption at the interface to a solid occurs in the presence of porous materials with
high surface area, particularly nanoporous solids. This phenomenon is exploited in several
processes of the chemical and energy industries; examples of relevant technologies include
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gas separation processes, such as air separation,1 CO2 capture2 and natural gas upgrading,3
heterogeneous catalysis, adsorption based heat pumps for solar cooling systems,4 hydrogen
storage,5 and CO2 storage in the subsurface with or without the recovery of hydrocarbons,
such as during coalbed methane6 or shale gas production.7 Because it strongly depends on
the geometric and chemico-physical properties of pore surfaces, gas adsorption has also de-
veloped into a well-established tool for the structural characterization of the porous solids
themselves. High-resolution experimental protocols are nowadays available that profitably
combine a range of sub-critical gases and that exploit their specific phase-behavior under
confinement.8,9 From the interpretation of a full adsorption/desorption isotherm, material-
specific metrics are extracted (e.g., surface area, pore volume, pore size distribution) that
are needed for the design and optimization of the processes described above. Most signifi-
cantly, progress in materials engineering research continues to trigger advances in this field,
such as for the textural characterization of new hierarchical adsorbent materials by phys-
ical adsorption10 and through the development of reliable molecular-scale models for data
interpretation.11 Despite these continued efforts, gas adsorption measurements still result
in average properties of the given sample and they fail at uncovering variabilities that are
known to exist over the continuum of relevant length scales. Recent developments in spectro-
scopic techniques (chemical imaging, see refs.12,13 for a comprehensive review on the topic)
have uncovered heterogeneities in terms of structure, composition and reactivity among sin-
gle adsorbent- and catalyst-particles. While these heterogeneities are inevitably linked to
both transport and adsorption properties of the porous particle, inter-particle heterogeneities
within a particle batch, and batch-to-batch variations are expected to complicate matters
even further. In this context, we contend that the ability to couple conventional adsorp-
tion experiments with the simultaneous imaging of the densification process could pave the
way towards (i) the multi-dimensional, multi-scale characterization of microporous solids
and (ii) a comprehensive understanding of the adsorption process over a range of relevant
length-scales. We refer to this new technology as digital adsorption. The latter is attractive
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from mainly two perspectives: on the one hand, because gas adsorption is mostly limited
to pores with dimensions of few nanometres, the ability to quantify it would extend the
range of operability of those imaging techniques that are limited in their spatial resolution
to a few microns and above. On the other hand, the use of the imaging technique itself
extends conventional gas adsorption techniques to multiple dimensions, hence providing for
an augmented characterization of microporous solids, while enabling in-situ and operando
evaluation of adsorption-based processes.
Among the plurality of available imaging techniques, most advances in the area of ad-
sorption over the last decade have been achieved through the use interference microscopy
(IFM).14 The latter enables observing local 2D concentration maps (where the concentration
is averaged along the third direction15) in single zeotype crystals during transient adsorp-
tion/desorption cycles16–18 with spatial and temporal resolutions on the order of micrometers
and seconds, respectively. While the direct quantification of adsorbed amounts still poses a
challenge, the measured relative concentration profiles have allowed for pivotal studies, where
evidence was indeed provided for the heterogeneous nature of adsorbent crystals and the cor-
responding variability in their uptake rate was quantified.19 Other remarkable attempts at
imaging the adsorbed phase have been carried out by X-ray computed tomography (CT).
The latter stands out for a number of key features: it is a truly 3D measurement technique;
it is an in-situ technique that can be applied operando 20 thanks to its non-invasive nature
and the possibility of using actual process gases; and its availability as bench/lab scale setup
is widespread, with instruments able to cover a wide range of resolutions and system sizes
from the micrometer (crystal size) to the meter (reactor size). In the following, we present a
brief review of works that have specifically addressed the study of adsorption by X-ray CT.
1.1 Imaging of gas adsorption with X-rays
The response of X-ray CT measurements depends largely on the bulk density of the imaged
object and most CT scanners operate in a way that measurements of the X-ray beam attenu-
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ation are taken for multiple sample orientations, which upon reconstruction provides data at
various spatial locations (voxels) within the object. The ability to quantify the local density
from X-ray CT scans makes it plausible to exploit this technique for the detection of the ad-
sorbed phase, which has a liquid-like density, hence a much larger density as compared to the
bulk gas phase. Evidence to this dates back to the mid-70s, when Dubinin et al. 21 visualized
the propagation of the adsorptive front of bromobenzene into zeolite particles with radio-
graphs. The realization that the dense adsorbed phase provides for attenuation contrast has
been exploited in more recent works; however, most of these studies were either purposely
qualitative21–23 or used a strongly attenuating component for imaging (e.g. Krypton,24,25
Xenon,26,27 brominated21 or chlorinated22,23 solvent vapors). As shown in Figure S1 (SI),
these radio-opaque components provide a 5- to 100-fold increase in attenuation as compared
to more conventional process gases (e.g., CO2). Only a limited number of studies have used
X-ray CT measurements to study adsorption quantitatively by providing critical elements
that support the use of this technique, such as (i) the validation of the X-ray measurement
with an independent adsorption experiment and (ii) the recognition that adsorption data
can be measured on a voxel-by-voxel level. Again, the picture is rather incomplete, as some
of these studies26,28 report solely on the measurement of total loadings, without differentiat-
ing between the bulk- and adsorbed-phase, while others24,25,27,29 do quantify adsorption, but
without referring to the truly measurable quantities in an adsorption experiment, namely
net and excess adsorbed amounts. Most significantly, they all lack of the proper estimation
of measurement uncertainties, which is a key requirement to justify the use of X-ray CT as a
novel tool for 3D adsorption experiments. It is only in a recent communication by Pini 30 that
these issues were tackled by providing both the operating equations and the experimental
protocol to measure excess adsorption using X-rays, and by validating them on a common
host-guest system, namely CO2 on zeolite 13X.
In this work, we build on these last findings by presenting and discussing digital adsorp-
tion experiments carried out for two adsorbate/adsorbent systems, namely CO2/zeolite 13X
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and CO2/activated carbon in the range of pressure 1–30 bar at 25 ◦C. Specifically, the aims of
this work are (i) to design a workflow for measuring excess adsorption isotherms from X-ray
CT scans, including a rigorous uncertainty analysis of the measurements; (ii) to present the
first 3D data set of adsorption isotherms measured at a resolution of 10mm3 on a laboratory
fixed-bed adsorption column; (iii) to validate the obtained experimental results by compar-
ison with independent data reported in the literature; and (iv) to assess the applicability of
this novel method for the measurement of gas adsorption isotherms on different classes of
natural and synthetic porous materials.
2 Theory
The response of a reconstructed X-ray CT image is the local linear attenuation coefficient,
µ, which is defined as the product between the bulk density of the scanned object, ρ, and
its mass attenuation coefficient, α:31 µ = αρ. In the energy range applied in X-ray CT
(30–140 keV), α is composed of the contributions from photoelectric effect (dominant at
E << 100 keV) and Compton scattering (dominant at E > 100 keV), and it depends on the
photon energy (spectrum) and the atomic properties of the scanned object. When the latter
is composed of a mixture of a certain number of phases (P ), the overall attenuation coefficient
µ is obtained by assuming ideal mixing and by using the attenuation coefficient/density
values of each individual phase k:
µ = ρP∑
k=1
wk
ρkµk =
P∑
k=1
φkµk (1)
where ρ is the density of the mixture, and wk and φk are the weight and the volumetric
fractions of phase k in the mixture, respectively. When a porous solid of bulk volume, Vtot,
with total pore space, Vpore, is exposed to an adsorptive “a”, surface forces will result in the
densification of the fluid at the interface to the solid phase, thus creating an adsorbed phase
with liquid-like density. Hence, the overall attenuation coefficient can be written as the sum
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of contributions from the bulk fluid, solid and adsorbed phases:
Vtotµa = (Vpore − Va)ρfαa + (Vtot − Vpore)ρsαs +madsαa (2)
where ρf and ρs are the densities of the bulk fluid and of the solid, respectively, and mads
is the absolute adsorbed mass. Note that because the fluid phase is a pure component, the
same proportionality constant, αa, is used for both the bulk fluid and adsorbed phase. Eq. 2
is rearranged by introducing an excess adsorption term, ηex:
µa = φtotµa + (1− φtot)µs + ηex (3)
where φtot = Vpore/Vtot is the total void fraction, and ηex is directly related to the truly
measurable quantity in an adsorption experiment, namely the surface excess32 mex = mads−
ρfV ads. It follows that:
ηex =mexαa
Vtot
= mexv αa (4)
wheremexv is the excess adsorbed amount per unit volume. The overall attenuation coefficient
of the same volume of porous solid exposed to an inert gas “i” is given by:
µi = φtotµi + (1− φtot)µs (5)
Upon subtraction of Eqs. (3) and (5) and rearranging, the following expression is obtained:
ηex(p, T ) = µa(p, T )− µi(p∗, T ∗)− φtot [µa(p, T )− µi(p
∗, T ∗)] (6)
where it can readily be observed that excess adsorption can be determined by combining
independent measurements (i.e., CT scans) of the porous solid exposed to the adsorptive
and inert gas, respectively, with prior knowledge of the attenuation of the pure fluids and
of the total void fraction30. In Eq. 6, the (p, T ) conditions were made explicit to emphasize
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that they may differ between the measurements with the adsorptive and the inert gas. In
this study, the latter are carried out for a single set of reference pressure (p∗ = 5bar)
and temperature (T ∗ = 25 ◦C). Hereby, the sole assumption is that the linear attenuation
coefficient of the solid phase, µs, takes the same value at both reference and experimental
conditions.
Some instruments, more particularly medical CT scanners, provide images reconstructed
in Hounsfield units (HU), or CT numbers, which are obtained from a linear combination
of the measured linear attenuation coefficients with values known from a calibration of the
instrument with suitable phantoms (e.g., water and air):
CT =µ− µwater
µwater − µair
1000 (7)
Eq. 6 can thus be rewritten in terms of CT numbers:
Hex(p, T ) = CT a(p, T )− CT i(p∗, T ∗)− φtot [CT a(p, T )− CT i(p
∗, T ∗)] (8)
The excess adsorbed mass can then be computed as:
mexv = Hex/aa (9)
where aa = 1000αa/(µwater − µair), can also be conveniently found from the slope of the
calibration curve, CT a = aaρf+b (see Experimental section). Eq. 8 and 9 provide the working
equations to determine adsorbed amounts from X-ray CT scans in terms of the typical
units used in conventional adsorption experiments. It is worth noting that these equations
are not restricted to a specific energy range provided that a negligible beam hardening is
present (sample exposed to a homogeneous energy spectrum), nor are they restricted to any
resolution. They are thus applied for each voxel in the system, whereas slice- or sample-
averaged properties are calculated using slice- or sample-averaged CT numbers. We also
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note that when working with commercial adsorbents, such as in this study, it is reasonable to
assume that the attenuation of the solid component takes a constant value, as these materials
are homogeneous in terms of skeletal density and composition at the spatial resolution of
medical CT scanners (mm and above). Because the average sample porosity can be measured
from independent experiments, the CT number of the solid can be estimated from Eq. 5
written in terms sample-averaged CT numbers:
CT s =CT i,avg(p∗, T ∗)− φtot,avgCT i(p∗, T ∗)
1− φtot,avg
(10)
The local porosity can then readily be estimated from Eq. 10 solved for each voxel in the
system:
φtot =CT s − CT i(p∗, T ∗)
CT s − CT i(p∗, T ∗)(11)
When spatial variations in composition are expected, such as with natural porous solids
or beds with mixed adsorbents, the assumption above needs to be relaxed and local porosity
values can be estimated from the subtraction of scans of the porous solid saturated with zero-
excess fluids, as is typically done with air and water for the determination of the porosity
map of rocks.33,34
3 Materials and methods
3.1 Materials and apparatus
The adsorption experiments were performed using the experimental setup depicted in Fig-
ure 1. A custom-made aluminum sample-holder (wall thickness: 1.35 cm) has been used that
can accommodate a cylindrical sample of 5 cm in diameter and of variable length. While it
is fairly translucent to X-rays, aluminum provides for the required mechanical strength and
reduces beam-hardening artifacts.35 The sample is located between two aluminum end-plates
with embedded circular grooves for enhanced fluid distribution upon injection. The sample-
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Table 1: Properties of the adsorbent materials and of the layered fixed-bed. Thebed density (ρbed) was calculated based on the mass of material and the measuredvolume (AL) occupied within the adsorbent column. The adsorbent material(skeletal) density (ρs) was obtained from the literature in the case of zeolites,30
and from a helium gravimetric measurement in the case of activated carbon(10–135 bar, 25 ◦C in a Rubotherm Magnetic Suspension Balance). The totalporosity of each layer is estimated as φtot,avg = 1− ρbed/ρs. The attenuation of thesolid is computed from Eq.10 applied to each layer of adsorbent, independently.
Glass beads Zeolite 13X Activated carbon
L (cm) 2.5 ± 0.3 3.4 ± 0.3 4.8 ± 0.3ρbed (g/cm3) 1.69 ± 0.13 0.672± 0.038 0.435± 0.018ρs (g/cm3) 2.65 ± 0.02 2.567± 0.040 2.16 ± 0.34φtot,avg (–) 0.36 ± 0.05 0.74 ± 0.02 0.80 ± 0.03CT s (HU) 2142± 292 1905± 164 1056± 315
layered bed was prepared by packing the adsorbents (glass beads / zeolites / activated
carbon) in the cylindrical sample holder under a gentle flow of helium, so as to avoid any
excessive contact of the materials with air, and subsequently kept under helium atmosphere
(ca. 5 bar). Each layer (2–4 cm in length) was separated by a stainless steel mesh, achieving
a total bed length L = 11 cm (properties listed in Table 1). After positioning it in the
scanner gantry, a full X-ray scan of the layered bed was taken (referred to as ‘Helium scan’)
and the sample holder was no longer moved for the whole duration of the experiment. The
gas adsorption experiments (referred to as ‘CO2 scans’) were carried out by both increasing
(1 bar, 3 bar, 6 bar, 10 bar, 15 bar, 20 bar and 30 bar) and decreasing (20 bar, 10 bar and
1 bar) the gas pressure in the sample holder; this was achieved by setting the inlet pressure
regulator to the desired level, while using the back-pressure valve to maintain a low CO2
flow through the bed, which was also kept during the scans. The flow rate was adjusted so
as to result in a negligible pressure drop along the bed. Adsorption equilibrium was achieved
after about 30min and was followed by the acquisition of a full X-ray scan of the layered
bed. For each adsorbent-layer and at each pressure step, an additional set of 10 repeated
scans were taken at selected locations (slices); as described in Pini and Madonna 34 , repeated
scans are very useful to assess image noise and to estimate the uncertainties in the computed
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adsorbed amounts. All images were acquired by applying a tube voltage of 120 kV, a current
of 200mA, a scan time of 1 s per slice and a (120 × 120) mm field of view (further details
on the CT setup are provided in section 2 the SI). Images were reconstructed with a (xyz)
resolution of (0.234 × 0.234 × 1) mm3 without applying any filter. Scanning of the entire
bed (11 cm) required ca. 10min, so that approximately 8 hours were required to measure
the 3D adsorption isotherms with 8 points. Image analysis and data processing were carried
out using in-house MATLAB codes.
3.2.1 Calibration and measurement uncertainty
As anticipated in the previous section, knowledge of the attenuation of each operating gas
(He and CO2) at experimental conditions (pressure and temperature) is needed to compute
adsorbed amounts using Eq. 8. To this aim, the empty sample-holder was filled with gas-
phase only and was imaged by acquiring 10 repeated scans at a given location using the
same imaging parameters applied for the adsorption experiments. Images were taken at
various pressures and over the same pressure range covered in the adsorption experiments.
As expected (and shown in Figure S2 of the SI), the attenuation in Hounsfield units is linearly
correlated to the density of the gas, i.e., CT k = akρf+b, where the constant parameters ak and
b were estimated by fitting to the respective sets of calibration experiments (k = {He,CO2},
values given in Table 2) and the density values at each measured pressure were obtained
from the NIST database.36 We note that this calibration procedure has to be carried out
only once (for a given sample-holder) and is somewhat analogous to the acquisition of a
reference measurement that is commonly needed for gravimetric or manometric adsorption
experiments. To estimate measurement uncertainties, the protocol described in Pini and
Madonna 34 was followed and details specific to the experiments reported here are presented
in the SI. Briefly, because the noise observed in CT images is random and uncorrelated
for voxel sizes larger than 500 µm3 (see Figure S3), classic rules of error propagation apply
and measurement error is estimated from the standard deviation observed in the (normal)
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Table 2: Calibration of the CT number as a function of density (CT k = akρf + b)for the pure component gases at 25 ◦C and over the pressure range 1–30 bar. CT
numbers were obtained by averaging readings for all voxels within a 5mm×1mmcircular mask (≈ 75 voxels). Parameters are reported as the best least-squareestimator and the corresponding 95% confidence interval. Note that differencesin the parameter b are within measurement error and the value (899 ± 1)HUwill be used throughout the study.
ak, (HUm3 kg−1) b, (HU)
CO2 0.871± 0.008 −898.9± 0.4He 0.73± 0.04 −899.1± 0.9
distribution of values obtained upon subtracting two images taken at identical locations.
As shown in Figure S4, the uncertainty associated with the measured CT number depends
on (i) average CT number (Figure S4a) and (ii) the voxel size (Figure S4b), and it can be
described by the following general equation (Figure S4c):
σCT = (c1CT + c2)vc3vox (12)
where the coefficients c1 = (3.18± 0.04)× 10−3, c2 = 6.36± 0.03, c3 = −0.331± 0.003 were
fitted to the CT noise obtained from the analysis of the repeated scans at various voxel
resolutions (1–103mm3). The uncertainty on the measured excess adsorption, σmexv
, ranges
between 2%rel. and 5%rel. for voxel sizes of 10mm3, and it is negligible for slice- and layer-
averaged values (σmexv
< 1%rel.). We note that the estimated values include a contribution
from the uncertainty in the estimated porosity (σφtot, see Eqs. S3 and S4 in the SI) of ±0.02
and ±0.03 for the zeolite and activated carbon layer, respectively.
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change with pressure (Hex ≈ 2.8HU, corresponding to ≈ 0.07mmol/cm3). In contrast, the
change in attenuation of the zeolite and activated carbon layers is significantly larger and
increases with pressure (zeolites: Hex = 112–142HU, corresponding to 2.9–3.7mmol/cm3;
activated carbon: Hex = 46–146HU, corresponding to 1.2–3.8mmol/cm3). This behavior
can be explained by the presence of a denser, liquid-like phase in the micropores of the two
materials, as would be indeed expected from the occurrence of CO2 adsorption.
Table 3: Layer-averaged CT attenuation expressed as difference between CO2
and helium scans, and obtained from the experiments with, CT a − CT i, andwithout adsorbent in the sample holder, −φtot(CT a−CT i). The latter representsthe contribution of the bulk phase in an adsorption experiment and the excessterm (Hex) is obtained as their sum. Layer-averaged CT numbers are given inHounsfield units [HU] and are computed by averaging all voxel readings withina section that is at least 20mm thick (shaded regions in Figure 3).
CO2 pressure 1 bar 15 bar 30 bar
Glass
CT a − CT i 2.82± 0.15 12.1 ± 0.2 24.7 ± 0.2−φtot(CT a − CT i) −0.04± 0.12 −9.7 ± 1.6 −21.5 ± 3.6Hex 2.78± 0.20 2.4 ± 1.6 3.2 ± 3.6
Zeolite 13X
CT a − CT i 111.72± 0.12 156.5 ± 0.1 185.6 ± 0.1−φtot(CT a − CT i) −0.08± 0.25 −19.8 ± 0.5 −43.6 ± 0.9Hex 111.60± 0.28 136.8 ± 0.5 142.0 ± 0.9
Activated Carbon
CT a − CT i 46.06± 0.11 149.7 ± 0.1 192.7 ± 0.1−φtot(CT a − CT i) −0.09± 0.27 −21.4 ± 0.9 −47.2 ± 1.9Hex 45.98± 0.29 128.3 ± 0.9 145.5 ± 1.9
4.2 Adsorption isotherms
Equilibrium adsorption isotherms are shown in Figure 4 that have been obtained upon
application of Eqs. 8 and 9 to the X-ray tomograms acquired at various CO2 pressures.
These have been obtained upon averaging all voxels values within a 20mm-long section of
each adsorbent layer (∼4000 voxels) and are reported in terms of molar excess adsorbed
amount per unit mass of adsorbent, nex = mexv /(ρbedMm). For all materials, differences
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the early uptake of gas and, accordingly, to a very steep isotherm that flattens out upon
reaching saturation. On the contrary, activated carbons (violet-colored symbols) possess a
distribution of pore sizes, with a significant fraction of both micro- (< 2 nm) and meso-
porosity (2–50 nm);47 accordingly, their adsorption isotherms are characterized by a more
gradual rise. Most significantly, the adsorption isotherms obtained in this study by X-ray
imaging are in good agreement with data reported in the literature at similar p, T conditions
and obtained using conventional techniques, such as the manometric and gravimetric meth-
ods (references provided in Table 4). In the figure, the latter are represented by the crosses,
which, for both materials, outline a fairly wide area, as indicated through color-shading. This
variability highlights once more issues presented in the Introduction, such as batch-to-batch
heterogeneities, differences in material suppliers and selection of regeneration conditions.
However, the general agreement between results from this study and the trends reported in
the literature in terms of both isotherm shape and adsorption loadings strongly supports the
reliability of our measurements and the suitability of X-ray CT for gas adsorption studies on
microporous solids. We note that while previous studies have indicated the potential of this
and other imaging techniques for measuring adsorption in porous materials, this is the first
time that isotherms have been fully resolved on commercial adsorbents using X-ray CT.
4.3 Multi-dimensional, multi-scale adsorption isotherms
In Figure 5, isotherms are shown for selected voxels within the central horizontal cross section
of the layered adsorbent bed (filled symbols) and that have been calculated by considering
three different voxel volumes, namely (a) 101mm3, (b) 102mm3 and (c) 103mm3. The
isotherms are reported in terms of molar excess adsorbed amount per unit bulk volume,
nexv = mex
v /Mm, and are compared to the corresponding layer-averaged curves discussed
previously (empty symbols, average of ∼4000 voxels). Error bars are also shown in each plot
and are only visible for the data acquired at the highest resolution. In agreement with the
results discussed in the previous section, it can be seen that isotherms measured on the two
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Table 4: Adsorbed amount of CO2at 25 ◦C and 1 bar on zeolite 13X and activated
carbon. Data from the literature are compared to results from this study (X-rayCT).
Reference Supplier Regeneration Method nex1bar [mol/kg]
Zeolite 13X
Siriwardane et al. 38 Zeochem 298K volumetric 3.6Hyun and Danner 37 Linde 467K volumetric 3.9Delgado et al. 42 Union Carbide 593K volumetric 4.1Cavenati et al. 39 CECA 593K gravimetric 4.6Bezerra et al. 40 Klostrolith 623K gravimetric 5.1Hefti et al. 41 Zeochem 673K gravimetric 5.4This work Zeochem 563K X-ray CT 4.5± 0.3
Activated Carbon
Schell et al. 45 Chemviron 423K gravimetric 1.6Delgado et al. 42 BPL 4X10 423K volumetric 1.8Dreisbach et al. 43 Norit R1 353K volumetric 2.2Millward and Yaghi 44 Norit RB2 573K gravimetric 2.5Singh and Kumar 46 Norit RB3 373K volumetric 3.0This work Norit RB3 423K X-ray CT 2.8± 0.1
materials differ significantly, thus reflecting their distinct adsorptive properties. Notably,
while they follow the same qualitative behavior as the layer-averaged data, the local (voxel-
specific) adsorption isotherms are relatively distinct from each other, thus indicating a degree
of variability in the adsorption properties of the packed bed at the mm-scale. The latter
decreases with increasing voxel size and the isotherms within each adsorbent become almost
indistinguishable for voxels with volume Vvox = 1 cm3. This result can be understood by
considering that also the void fraction in each voxel differs, and that in a random pack this
variability decreases upon increasing the volume of the spatial domain of interest.49
The analysis presented above is extended by probing the variability in the adsorption
properties of the two adsorbents across a continuum of length scales, i.e. in the range 10−1–
105mm3. This is illustrated in Figure 6 in the form of so-called representative elementary
volume (REV) curves50 that have been obtained here by calculating the adsorbed amount at
30 bar within a volume that is grown from a single voxel (with volume (0.5× 0.5× 1) mm3)
up to the total volume of the adsorbent layer. In the figure, eleven REV curves with randomly
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distributed starting points are shown alongside boxplots that display distributions at specific
voxel sizes, namely 1mm3, 101mm3, 102mm3 and 103mm3 (line: median, box: interquartile
range, whiskers: 95% range). For both materials, the REV curves and the boxplots indicate
a very similar behavior. For small voxel sizes (<10mm3), local variations in the adsorbed
amount are large: at 1mm3, nexv ranges between 2–5.5mmol/cm3 for zeolite 13X (45% relative
deviation from the mean) and between 1.2–6.5mmol/cm3 for activated carbon (65% relative
deviation from the mean). As the voxel size increases, the distribution becomes narrower
until it entirely falls in a range that lies within 5% deviation from the mean (indicated by
the color-shaded regions). For zeolite 13X, this point is attained at a voxel size of 102mm3,
while voxel sizes of at least 103mm3 are required to observe uniform adsorption in activated
carbon. For both materials these distinct voxel sizes correspond to 3–4 particles per voxel
edge, as indicated by the secondary x-axis. This number agrees very well with the attainment
of a REV for the porosity of a random pack of uniform glass beads.49 Packing effects are
thus expected to contribute to a greater extent in the variability of the adsorbed amount at
scales for which the voxel size is comparable to the size of the adsorbent pellets.
5 Discussion
Gas adsorption has established itself as a practical and reliable tool for the structural charac-
terization of microporous solids. Over the years, experimental protocols have been developed
that allow the practitioner to make use of a variety of gases and organic vapors to selectively
probe the pore-space of the material under investigation. Accordingly, approaches are avail-
able nowadays that enable extracting parameters, such as pore volumes, pore-size distribu-
tion and surface areas, which serve as a fingerprint of the adsorbent. The coupling of these
standard approaches with the simultaneous imaging of adsorption by X-ray CT adds a new
dimension to adsorption-based techniques by providing an unprecedented level of observa-
tional detail on both material properties and the adsorption process itself. In the following,
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we discuss two technical developments: (i) the measurement of spatially resolved adsorption
isotherms and their use for quantifying adsorption heterogeneity; (ii) the extension of the
X-ray CT technique to a range of porous solids, including weakly adsorbing materials, such
as microporous rocks.
5.1 Adsorption heterogeneity
5.1.1 Voxel-by-voxel adsorption isotherms and scaling
One of the benefits arising from the application of a tomographic technique for measuring
adsorption is the ability to make observations over multiple spatial dimensions and, accord-
ingly, to access spatially resolved adsorption isotherms and parameters. Figure 7a shows
the whole population of adsorption isotherms measured within the zeolite (3060 isotherms)
and activated carbon layers (4540 isotherms) at a resolution of 10mm3. These are plotted
alongside the adsorption isotherms representative of each adsorbent layer (empty symbols),
outlining a type I isotherm, which is typically described by the Langmuir isotherm model
(black lines in the figure):47
nexv =
n∞Kp
1 +Kp(13)
where the parameters n∞ and K are the saturation capacity and the affinity coefficient, re-
spectively, both of which depend on the adsorbent type (fitted parameters values are provided
in the figure caption). At any given pressure and for both materials, the spread of adsorption
loadings at the voxel-scale is significant: at 20 bar, nexv ranges between 2.8–4.2mmol/cm3 for
zeolite 13X (20% relative deviation from the mean) and between 1.8–2.5mmol/cm3 for ac-
tivated carbon (50% relative deviation from the mean). These variations are significantly
larger than the predicted uncertainty in the measured adsorbed amount at the same scale
(3% and 5% relative deviation from the mean for zeolite 13X and activated carbon, re-
spectively) and reflect therefore true spatial variabilities in the adsorption properties of the
adsorbent bed. Nevertheless, all isotherms retain the characteristic shape outlined by the
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layer-averaged curve and Eq. 13 can thus be used to describe each isotherm by fitting the set
of parameters n∞
j and Kj for each voxel j independently. As a validation of this approach, all
isotherms are again plotted in Figure 7b in terms of a scaled adsorbed amount, nexv,j(p)/n
∞
j ,
and by using Kjp as the new independent variable; to facilitate comparison with the unscaled
data, units are re-established by multiplication with the layer-averaged isotherm parameters
n∞
avg and 1/Kavg, respectively. It can be seen that all data points now collapse around two
distinct curves that describe activated carbon and zeolite adsorption data; the effectiveness
of the scaling is quantified through the Spearman rank correlation, which increases from
≈ 0.8 for the unscaled data to > 0.95 for the scale data, and through the value of the sum
of squared residuals with respect to the fitted Langmuir isotherms, which is reduced to only
11% (for zeolites) and 4% (for activated carbon) of the value for the unscaled data. In
practice, this result indicates that, within each adsorbent layer, voxels can be considered
similar (with reference to the early work by Miller and Miller 51) in terms of their adsorptive
properties, which in this case are fully characterized through pairs of spatially distributed
scaling factors, namely n∞
avg/n∞
j and Kj/Kavg. Accordingly, the scaling exercise yields two
separate universal adsorption isotherm curves, Γex(ξ), that are descriptive of all voxels in
the given adsorbate-adsorbent system and that take the following form:
Γex =ξ
1 + ξ(14)
where Γex = nexv,j(p)(n
∞
avg/n∞
j ) and ξ = p(Kj/Kavg). We note that the scaling approach
applied here to spatially distributed isotherms is analogous to the adoption of the so-called
generalized (or characteristic) adsorption curve that correlate adsorption isotherms of a given
adsorbate/adsorbent pair at different temperatures52 or of different adsorbates onto one
adsorbent.53
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affinity coefficient could arise from a random distribution of the free energy of adsorption,
∆G∗
ads. As shown through the mathematical derivation provided in section 5 of the SI, the
latter is directly related to the thermodynamic affinity coefficient K ′, which for an ideal gas
and an ideal adsorbed phase is equal to the Langmuir affinity coefficient, K:54
∆G∗
ads = −RT ln (K ′) ≡ −RT ln(K) (15)
Thus, while we cannot exclude a priori that it is an artifact arising from the non-linear fit
to uncertain data55, the observed distribution may also be reflecting the true physical vari-
ability of the adsorbent particles themselves, as it would be expected from physico-chemical
variations among or within the pellets. Support to this hypothesis is also the fact that a
variation of similar extent in the affinity coefficient is obtained upon analyzing isotherms
reported in the literature on the same materials, which are very likely due to discrepancies
in modes of adsorbent regenerations and/or batch-to-batch heterogeneities. Further inves-
tigations on this topic are necessary to thoroughly understand the origin and scale of the
physico-chemical heterogeneity of the adsorbent material and particles. A first step in this
direction could follow from the interpretation of 3D digital adsorption experiments carried
out at higher resolution, e.g. with the use of a micro-CT, thus allowing to decouple the
effect of packing (or bed heterogeneity) from material heterogeneity by resolving individual
particles, and computing adsorption isotherms for individual particles.
5.2 Digital adsorption: applicability to different materials
Because gas adsorption still represents the gold standard for the characterisation of microp-
orous solids, advancements are continuously being made to refine measurement protocols and
interpretation of the obtained adsorption isotherms.9 Experiments typically involve measur-
ing the excess adsorption of small gases, e.g. N2, Ar, Kr and/or CO2, under sub-critical
conditions, and at pressures ranging from vacuum to 1 bar. These measurements, from
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which pore volume, specific surface area and pore size distribution can be obtained, have
become routine practice in the characterization of novel adsorbent materials,10 catalysts56
and natural microporous materials, including coals,57 carbonates,58,59 clays and shales.60 To
assess the applicability of X-ray CT for measuring gas adsorption isotherms on a variety
of materials, we discuss in the following the expected measurement uncertainties that have
been estimated by considering the adsorption of CO2 on a generic nanoporous material at
conditions representative of sub-critical adsorption measurements (0 ◦C and p = 1bar). The
analysis is intended to help the adsorption practitioner to design an experiment using a
conventional medical CT scanner, so as to achieve the required precision at given spatial
resolution.
If the pressure is sufficiently low, the gas behaves ideally and the second term in Eq.
8 can be dropped (i.e., φtot(CT a − CT i) ≈ 030), hence the estimation of uncertainties in
the measured adsorbed amount is greatly simplified (see Eqs. S5 and S6 in the SI). For
the calculations, we consider a packed bed (φbed = 0.37) of a given adsorbent material
with uniform and constant attenuation of the solid component (CT s = 2000HU). We
note that for some of the “lighter” materials (e.g., carbons), this assumption will lead to an
overestimation of the measurement uncertainty and the results reported below are thus to be
considered as upper bounds. We further assume that the intraparticle porosity is composed
of a fraction of micro-/meso-pores (φm) that contribute to adsorption, and a fraction of larger
meso-/macro-pores (φM) with negligible surface area, such that the total porosity is given
by φtot = φbed + (1− φbed)(φm + φM). The variability among different classes of adsorbent
materials is introduced by considering typical pore volumes reported in the literature, which
are linked to the adsorption capacity by assuming a constant value for the density of the
adsorbed phase (21.1mol/L, taken as the liquid density of CO2 at 0 ◦C36). The amount
of macroporosity is obtained by assuming a ratio φm : φM of 60 : 40, which is typical for
materials produced in pelletized form, such as commercial zeolites.48
A contour plot is presented in Figure 9 for the obtained total relative error as a function
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of the adsorbed amount and of the voxel size. Not surprisingly and for a given voxel size, the
relative error decreases with increasing adsorption. Similarly, for a given amount adsorbed,
the error decreases with increasing voxel size, due to the averaging associated with image
coarsening. In the figure, various classes of materials are also represented by considering
their characteristic pore volumes (φm(1− φbed), scale shown on top of the figure). It can be
seen that commercial adsorbent materials (MOF, AC and zeolites) fall in a range where the
predicted relative error is fairly small (ca. 1–5%rel., for any voxel size), while the measure-
ment of adsorption isotherms on natural porous materials is affected by a larger uncertainty.
Specifically, the error for clays is maintained below 10%rel. for voxel sizes that are larger
than 10mm3, while much larger voxels are required for coal and shales (> 100mm3). The
reason for this is twofold: first, high-density materials are prone to a larger measurement
uncertainty, because CT noise is proportional to the attenuation of the packed bed, hence to
its density. Owing to their large volumetric capacity and low bed density, commercial ma-
terials therefore tend to be more suited for adsorption measurements by X-ray CT. Second,
materials such as clays or shales have lower porosity and hence a smaller adsorption capacity,
which translate into a larger relative error on the measured adsorbed amount, an issue that
is shared with the most common adsorptive characterization techniques.61 We note that in
such cases, the averaging of N repeated scans acquired at identical locations would decrease
the measurement error significantly without increasing the experiment complexity. Hence,
the predicted measurement errors shown in Figure 9 would decrease by a factor√N , as
suggested by standard rules of error propagation, which apply to variables that are normally
distributed (such as the CT noise34). These observations suggest that the X-ray CT method
can indeed be applied to a range of microporous materials and provide reliable estimates of
the adsorbed amount over a continuum of relevant length-scales. It is worth noting that the
presented uncertainty figures are specific for the imaging settings used in this work (X-ray
tube voltage, resolution, and core holder), and for the considered operating conditions (0 ◦C
and p = 1bar). However, because the applied methodology and the considerations above
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probing the adsorption process in three dimensions and these data are the first of a kind to di-
rectly and non-destructively measure spatially-resolved adsorption isotherms on commercial
adsorbents. This novel ability was exploited to investigate adsorption heterogeneity within
the fixed-bed at a spatial resolution of 10mm3. A scaling approach was applied to analyze the
whole population of measured adsorption isotherms (7600), leading to a single universal ad-
sorption isotherm curve that is descriptive of all voxels for a given adsorbate/adsorbent pair.
From the scale dependent analysis of the adsorption heterogeneity (in the range of 1mm3 to
1 cm3), packing heterogeneity was identified as the main contributor to the observed spatial
variability, which was larger for the activated carbon rods as compared to the zeolite pellets.
Yet, significant variations in the affinity coefficient were observed for both adsorbents, which
could indicate true physico-chemical variations among the adsorbent particles.
A peculiarity of this study is that the experiments have been carried out using a ‘clas-
sic’ setting, namely a probing gas (CO2) that is not radio-opaque, and a packed column
with dimensions representative of a typical lab-scale fixed bed operating up to 30 bar. Its
applicability to different classes of materials was assessed by quantification of the expected
measurement uncertainty. Thereby, we have shown that the technique is readily applica-
ble to a large spectrum of commercial porous solids and that it can be extended to weakly
adsorbing materials with appropriate protocols that reduce measurement uncertainties. As
such, the obtained results encourage a wider use digital adsorption and we see three areas in
which it could contribute to the field of adsorptive characterization of porous solids. Firstly,
the proven ability to measure a multitude of different materials concurrently enables high-
throughput screening analyses, where the number of pressure sensors is decoupled from the
number of materials. Second, the non-invasive, multidimensional nature of the technique
enables probing the adsorption process operando and could be applied to reveal packing
deficiencies, the occurrence and location of adsorbent poisoning within a fixed-bed setup,
or the extent of propagation of an adsorption front during a dynamic experiment. Finally,
the ability to couple conventional sub-critical gas adsorption experiments and interpretation
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with X-ray CT imaging could pave the way towards the 3D characterization of porous sys-
tems at resolutions spanning multiple length-scales – from the micro-meter to the meter.
Such experiments are needed for the systematic design of formulation processes and scale-up
of nanoporous solids into shaped structures, such as pellets, monoliths or foams.
Acknowledgement
This work was carried out as part of the Qatar Carbonates and Carbon Storage Research
Centre (QCCSRC). We gratefully acknowledge the funding of QCCSRC provided jointly by
Qatar Petroleum, Shell, and the Qatar Science and Technology Park. RP also acknowledges
financial support from the Royal Society (Research Grant RG150277).
Supporting Information Available
Attenuation coefficients of relevant gases; Imaging parameters; Calibration curves; Analysis
of the CT noise; Measurement uncertainty quantification. This material is available free of
charge via the Internet at http://pubs.acs.org/.
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